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We introduce the notion of m-sparse power series (e.g. expanding sinx and cosx at x=0 gives 2-sparse power series: a coefficient an of the series can be nonzero only if remainder (n,2) is equal to a fixed number). Then we consider the problem of finding all m-points of a linear ordinary differential equation Ly=0 with polynomial coefficients (i.e., the points at which the equation has a solution in...
Let L(y)=0 be a linear homogeneous ordinary differential equation with polynomial coefficients. One of the general problems connected with such an equation is to find all points a (ordinary or singular) and all formal power series n=0~ c n (x-a) n which satisfy L(y)=0 and whose coefficient c n - considered as a function of n - has some 'nice' properties:...
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